Prepare the Carrots: If using regular carrots, peel and slice them into evenly sized pieces. If using baby carrots, no additional prep is needed.
Melt Butter: In a large skillet, melt the unsalted butter over medium heat.
Add Brown Sugar: Stir in the brown sugar, allowing it to melt and create a syrup-like consistency, approximately 1-2 minutes.
Incorporate Spices: Add the cinnamon and nutmeg to the butter and sugar mixture, stirring to combine.
Add Carrots and Broth: Add the carrots to the skillet, then pour in the vegetable broth. Mix well to coat the carrots in the glaze.
Cook the Carrots: Cover the skillet and reduce the heat to medium-low. Cook for about 10-15 minutes, stirring occasionally, until the carrots are tender and the glaze has thickened.
Season and Serve: Season with salt and pepper to taste. Garnish with freshly chopped parsley if desired.